Electrical grids, for instance the European electrical grid, may consist of a multiplicity of sub-grids. For instance, the German electrical grid is a sub-grid within the European electrical grid. This sub-grid may itself consist of various sub-grids. For instance, the German electrical grid includes a sub-grid for supplying the urban area of the city of Hamburg and a sub-grid for supplying the Munich urban area. Each sub-grid consists of a plurality of nodes or power supply buses, which are connected to one another via lines. Power generators and consumers or loads may be connected to the nodes. It is also possible, however, for subnetworks, which are hierarchically lower-level sub-grids of the sub-grid, to be connected to the nodes. Each sub-grid may in itself already have a relatively high complexity. The loads may be aggregated loads, for example, the power supply load of a housing estate or factory. The power generators, for example, are gas turbines or coal-fired power stations. The subnetworks may in turn consist of a plurality of nodes connected to one another via lines, to which nodes are attached power generators, loads, or sub-subnetworks. The various distribution grids may be connected to one another via high-voltage transmission grids.
Distributed renewable and, in some cases, also controllable electricity generators or power generators are being used increasingly in electrical grids. A possible result of this, for instance, is that in a country such as Germany, the maximum possible amount of power generated by renewable energy sources reaches or even exceeds the magnitude of the total load of the country. For instance, depending on weather conditions, the power generated by the renewable energy sources may surpass at least temporarily, for instance, for hours or weeks, the total consumption of power in the country concerned, in particular given future expansion of the electrical grids by deployment of further renewable energy sources.
With conventional electrical grids such as those currently in use, however, there is a problem with the further expansion of the electrical grid by renewable energy sources in that a certain proportion of conventional power generators, in particular coal-fired power stations or nuclear power stations, are needed in order to achieve grid stability. The grid stability is analyzed, for example, on the basis of dynamically non-linear simulations of the transmission grid. These non-linear simulations are based on detailed models of a relatively small number of conventional power generators. The loads contained in the electrical grid may be represented by distribution-grid areas containing connected or aggregated loads and a few non-controlled distributed generators. The grid stability is achieved by operating the conventional power generators according to suitable active-power and reactive-power rules. The larger the number of different distributed, in particular renewable, power generators, within the grid, the less possible it becomes to achieve or provide stability of the entire interconnected grid using the conventional techniques, in particular simulation techniques.